# Standard library header <valarray>

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This header is part of the numeric library.

### Includes
<initializer_list> (C++11) | std::initializer_list class template
### Classes
valarray | Numeric arrays and array slices (class template)
slice | BLAS-like slice of a valarray: starting index, length, stride (class)
slice_array | proxy to a subset of a valarray after applying a slice (class template)
gslice | generalized slice of a valarray: starting index, set of lengths, set of strides (class)
gslice_array | proxy to a subset of a valarray after applying a gslice (class template)
mask_array | proxy to a subset of a valarray after applying a boolean mask `operator[]` (class template)
indirect_array | proxy to a subset of a valarray after applying indirect `operator[]` (class template)
### Functions
##### Operations
std::swap(std::valarray) (C++11) | specializes the std::swap algorithm (function template)
std::begin(std::valarray) (C++11) | overloads std::begin (function template)
std::end(std::valarray) (C++11) | specializes std::end (function template)
operator+operator-operator*operator/operator%operator&operator|operator^operator<<operator>>operator&&operator|| | applies binary operators to each element of two valarrays, or a valarray and a value (function template)
operator==operator!=operator<operator<=operator>operator>= | compares two valarrays or a valarray with a value (function template)
abs(std::valarray) | applies the function abs to each element of valarray (function template)
##### Exponential functions
exp(std::valarray) | applies the function std::exp to each element of valarray (function template)
log(std::valarray) | applies the function std::log to each element of valarray (function template)
log10(std::valarray) | applies the function std::log10 to each element of valarray (function template)
##### Power functions
pow(std::valarray) | applies the function std::pow to two valarrays or a valarray and a value (function template)
sqrt(std::valarray) | applies the function std::sqrt to each element of valarray (function template)
##### Trigonometric functions
sin(std::valarray) | applies the function std::sin to each element of valarray (function template)
cos(std::valarray) | applies the function std::cos to each element of valarray (function template)
tan(std::valarray) | applies the function std::tan to each element of valarray (function template)
asin(std::valarray) | applies the function std::asin to each element of valarray (function template)
acos(std::valarray) | applies the function std::acos to each element of valarray (function template)
atan(std::valarray) | applies the function std::atan to each element of valarray (function template)
atan2(std::valarray) | applies the function std::atan2 to a valarray and a value (function template)
##### Hyperbolic functions
sinh(std::valarray) | applies the function std::sinh to each element of valarray (function template)
cosh(std::valarray) | applies the function std::cosh to each element of valarray (function template)
tanh(std::valarray) | applies the function std::tanh to each element of valarray (function template)

### Synopsis

    #include <initializer_list>

    namespace std {
      template<class T> class valarray;         // An array of type T
      class slice;                              // a BLAS-like slice out of an array
      template<class T> class slice_array;
      class gslice;                             // a generalized slice out of an array
      template<class T> class gslice_array;
      template<class T> class mask_array;       // a masked array
      template<class T> class indirect_array;   // an indirected array

      template<class T> void swap(valarray<T>&, valarray<T>&) noexcept;

      template<class T> valarray<T> operator* (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator* (const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator* (const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator/ (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator/ (const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator/ (const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator% (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator% (const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator% (const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator+ (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator+ (const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator+ (const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator- (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator- (const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator- (const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator^ (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator^ (const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator^ (const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator& (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator& (const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator& (const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator| (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator| (const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator| (const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator<<(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator<<(const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator<<(const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<T> operator>>(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> operator>>(const valarray<T>&,
                                               const typename valarray<T>::value_type&);
      template<class T> valarray<T> operator>>(const typename valarray<T>::value_type&,
                                               const valarray<T>&);

      template<class T> valarray<bool> operator&&(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<bool> operator&&(const valarray<T>&,
                                                  const typename valarray<T>::value_type&);
      template<class T> valarray<bool> operator&&(const typename valarray<T>::value_type&,
                                                  const valarray<T>&);

      template<class T> valarray<bool> operator||(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<bool> operator||(const valarray<T>&,
                                                  const typename valarray<T>::value_type&);
      template<class T> valarray<bool> operator||(const typename valarray<T>::value_type&,
                                                  const valarray<T>&);

      template<class T> valarray<bool> operator==(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<bool> operator==(const valarray<T>&,
                                                  const typename valarray<T>::value_type&);
      template<class T> valarray<bool> operator==(const typename valarray<T>::value_type&,
                                                  const valarray<T>&);
      template<class T> valarray<bool> operator!=(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<bool> operator!=(const valarray<T>&,
                                                  const typename valarray<T>::value_type&);
      template<class T> valarray<bool> operator!=(const typename valarray<T>::value_type&,
                                                  const valarray<T>&);

      template<class T> valarray<bool> operator< (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<bool> operator< (const valarray<T>&,
                                                  const typename valarray<T>::value_type&);
      template<class T> valarray<bool> operator< (const typename valarray<T>::value_type&,
                                                  const valarray<T>&);
      template<class T> valarray<bool> operator> (const valarray<T>&, const valarray<T>&);
      template<class T> valarray<bool> operator> (const valarray<T>&,
                                                  const typename valarray<T>::value_type&);
      template<class T> valarray<bool> operator> (const typename valarray<T>::value_type&,
                                                  const valarray<T>&);
      template<class T> valarray<bool> operator<=(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<bool> operator<=(const valarray<T>&,
                                                  const typename valarray<T>::value_type&);
      template<class T> valarray<bool> operator<=(const typename valarray<T>::value_type&,
                                                  const valarray<T>&);
      template<class T> valarray<bool> operator>=(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<bool> operator>=(const valarray<T>&,
                                                  const typename valarray<T>::value_type&);
      template<class T> valarray<bool> operator>=(const typename valarray<T>::value_type&,
                                                  const valarray<T>&);

      template<class T> valarray<T> abs  (const valarray<T>&);
      template<class T> valarray<T> acos (const valarray<T>&);
      template<class T> valarray<T> asin (const valarray<T>&);
      template<class T> valarray<T> atan (const valarray<T>&);

      template<class T> valarray<T> atan2(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> atan2(const valarray<T>&,
                                          const typename valarray<T>::value_type&);
      template<class T> valarray<T> atan2(const typename valarray<T>::value_type&,
                                          const valarray<T>&);

      template<class T> valarray<T> cos  (const valarray<T>&);
      template<class T> valarray<T> cosh (const valarray<T>&);
      template<class T> valarray<T> exp  (const valarray<T>&);
      template<class T> valarray<T> log  (const valarray<T>&);
      template<class T> valarray<T> log10(const valarray<T>&);

      template<class T> valarray<T> pow(const valarray<T>&, const valarray<T>&);
      template<class T> valarray<T> pow(const valarray<T>&,
                                        const typename valarray<T>::value_type&);
      template<class T> valarray<T> pow(const typename valarray<T>::value_type&,
                                        const valarray<T>&);

      template<class T> valarray<T> sin  (const valarray<T>&);
      template<class T> valarray<T> sinh (const valarray<T>&);
      template<class T> valarray<T> sqrt (const valarray<T>&);
      template<class T> valarray<T> tan  (const valarray<T>&);
      template<class T> valarray<T> tanh (const valarray<T>&);

      template<class T> /* unspecified1 */ begin(valarray<T>& v);
      template<class T> /* unspecified2 */ begin(const valarray<T>& v);
      template<class T> /* unspecified1 */ end(valarray<T>& v);
      template<class T> /* unspecified2 */ end(const valarray<T>& v);
    }

### Class template std::valarray

    namespace std {
      template<class T> class valarray {
      public:
        using value_type = T;

        // construct/destroy
        valarray();
        explicit valarray(size_t);
        valarray(const T&, size_t);
        valarray(const T*, size_t);
        valarray(const valarray&);
        valarray(valarray&&) noexcept;
        valarray(const slice_array<T>&);
        valarray(const gslice_array<T>&);
        valarray(const mask_array<T>&);
        valarray(const indirect_array<T>&);
        valarray(initializer_list<T>);
        ~valarray();

        // assignment
        valarray& operator=(const valarray&);
        valarray& operator=(valarray&&) noexcept;
        valarray& operator=(initializer_list<T>);
        valarray& operator=(const T&);
        valarray& operator=(const slice_array<T>&);
        valarray& operator=(const gslice_array<T>&);
        valarray& operator=(const mask_array<T>&);
        valarray& operator=(const indirect_array<T>&);

        // element access
        const T&          operator[](size_t) const;
        T&                operator[](size_t);

        // subset operations
        valarray          operator[](slice) const;
        slice_array<T>    operator[](slice);
        valarray          operator[](const gslice&) const;
        gslice_array<T>   operator[](const gslice&);
        valarray          operator[](const valarray<bool>&) const;
        mask_array<T>     operator[](const valarray<bool>&);
        valarray          operator[](const valarray<size_t>&) const;
        indirect_array<T> operator[](const valarray<size_t>&);

        // unary operators
        valarray operator+() const;
        valarray operator-() const;
        valarray operator~() const;
        valarray<bool> operator!() const;

        // compound assignment
        valarray& operator*= (const T&);
        valarray& operator/= (const T&);
        valarray& operator%= (const T&);
        valarray& operator+= (const T&);
        valarray& operator-= (const T&);
        valarray& operator^= (const T&);
        valarray& operator&= (const T&);
        valarray& operator|= (const T&);
        valarray& operator<<=(const T&);
        valarray& operator>>=(const T&);

        valarray& operator*= (const valarray&);
        valarray& operator/= (const valarray&);
        valarray& operator%= (const valarray&);
        valarray& operator+= (const valarray&);
        valarray& operator-= (const valarray&);
        valarray& operator^= (const valarray&);
        valarray& operator|= (const valarray&);
        valarray& operator&= (const valarray&);
        valarray& operator<<=(const valarray&);
        valarray& operator>>=(const valarray&);

        // member functions
        void swap(valarray&) noexcept;

        size_t size() const;

        T sum() const;
        T min() const;
        T max() const;

        valarray shift (int) const;
        valarray cshift(int) const;
        valarray apply(T func(T)) const;
        valarray apply(T func(const T&)) const;
        void resize(size_t sz, T c = T());
      };

      template<class T, size_t cnt> valarray(const T(&)[cnt], size_t) -> valarray<T>;
    }

### Class std::slice

    namespace std {
      class slice {
      public:
        slice();
        slice(size_t, size_t, size_t);

        size_t start() const;
        size_t size() const;
        size_t stride() const;

        friend bool operator==(const slice& x, const slice& y);
      };
    }

### Class template std::slice_array

    namespace std {
      template<class T> class slice_array {
      public:
        using value_type = T;

        void operator=  (const valarray<T>&) const;
        void operator*= (const valarray<T>&) const;
        void operator/= (const valarray<T>&) const;
        void operator%= (const valarray<T>&) const;
        void operator+= (const valarray<T>&) const;
        void operator-= (const valarray<T>&) const;
        void operator^= (const valarray<T>&) const;
        void operator&= (const valarray<T>&) const;
        void operator|= (const valarray<T>&) const;
        void operator<<=(const valarray<T>&) const;
        void operator>>=(const valarray<T>&) const;

        slice_array(const slice_array&);
        ~slice_array();
        const slice_array& operator=(const slice_array&) const;
        void operator=(const T&) const;

        slice_array() = delete;     // as implied by declaring copy constructor above
      };
    }

### Class std::gslice

    namespace std {
      class gslice {
      public:
        gslice();
        gslice(size_t s, const valarray<size_t>& l, const valarray<size_t>& d);

        size_t           start() const;
        valarray<size_t> size() const;
        valarray<size_t> stride() const;
      };
    }

### Class template std::gslice_array

    namespace std {
      template<class T> class gslice_array {
      public:
        using value_type = T;

        void operator=  (const valarray<T>&) const;
        void operator*= (const valarray<T>&) const;
        void operator/= (const valarray<T>&) const;
        void operator%= (const valarray<T>&) const;
        void operator+= (const valarray<T>&) const;
        void operator-= (const valarray<T>&) const;
        void operator^= (const valarray<T>&) const;
        void operator&= (const valarray<T>&) const;
        void operator|= (const valarray<T>&) const;
        void operator<<=(const valarray<T>&) const;
        void operator>>=(const valarray<T>&) const;

        gslice_array(const gslice_array&);
        ~gslice_array();
        const gslice_array& operator=(const gslice_array&) const;
        void operator=(const T&) const;

        gslice_array() = delete;    // as implied by declaring copy constructor above
      };
    }

### Class template std::mask_array

    namespace std {
      template<class T> class mask_array {
      public:
        using value_type = T;

        void operator=  (const valarray<T>&) const;
        void operator*= (const valarray<T>&) const;
        void operator/= (const valarray<T>&) const;
        void operator%= (const valarray<T>&) const;
        void operator+= (const valarray<T>&) const;
        void operator-= (const valarray<T>&) const;
        void operator^= (const valarray<T>&) const;
        void operator&= (const valarray<T>&) const;
        void operator|= (const valarray<T>&) const;
        void operator<<=(const valarray<T>&) const;
        void operator>>=(const valarray<T>&) const;

        mask_array(const mask_array&);
        ~mask_array();
        const mask_array& operator=(const mask_array&) const;
        void operator=(const T&) const;

        mask_array() = delete;      // as implied by declaring copy constructor above
      };
    }

### Class template std::indirect_array

    namespace std {
      template<class T> class indirect_array {
      public:
        using value_type = T;

        void operator=  (const valarray<T>&) const;
        void operator*= (const valarray<T>&) const;
        void operator/= (const valarray<T>&) const;
        void operator%= (const valarray<T>&) const;
        void operator+= (const valarray<T>&) const;
        void operator-= (const valarray<T>&) const;
        void operator^= (const valarray<T>&) const;
        void operator&= (const valarray<T>&) const;
        void operator|= (const valarray<T>&) const;
        void operator<<=(const valarray<T>&) const;
        void operator>>=(const valarray<T>&) const;

        indirect_array(const indirect_array&);
        ~indirect_array();
        const indirect_array& operator=(const indirect_array&) const;
        void operator=(const T&) const;

        indirect_array() = delete;  // as implied by declaring copy constructor above
      };
    }

### Defect reports

The following behavior-changing defect reports were applied retroactively to previously published C++ standards.

DR | Applied to | Behavior as published | Correct behavior
--- | --- | --- | ---
LWG 125 | C++98 | the return type of `valarray<T>::operator!()` was valarray<T> in the synopsis | corrected to valarray<bool>

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